Spin Seebeck Research Articles

Spin Seebeck effect and phonon energy transfer in heterostructures containing layers of a normal metal and a ferromagnetic insulator

In the framework of the kinetic approach based on the Boltzmann equation for the phonon distribution function, we analyze phonon heat transfer in a heterostructure containing a layer of a normal metal ($ N $) and a layer of a ferromagnetic insulator ($ F $). Two realistic methods for creating a temperature gradient in such a heterostructure are considered: by heating of the $N$-layer by an electric current and by placing the $N/F$-bilayer between massive dielectrics with different temperatures. The electron temperature $ T_e $ in the $ N $-layer and the magnon temperature $ T_m $ in the $ F $-layer are calculated. The difference in these temperatures determines the voltage $ V_{ISHE} $ on the $ N $-layer in the Seebeck spin effect regime. The dependence of $ V_{ISHE} $ on the bath temperature and on the thickness of the $ N $ and $ F $ layers is compared with the available experimental data.

Preparation of thulium iron garnet ceramics and investigation of spin transport properties in thin films

Compensated ferrimagnetic thulium iron garnet ceramics were prepared by the sol-gel method, which is significantly better than conventional solid-state reactions. Saturation magnetization yielded a maximum of 16.7 emu/g for specimens sintered at 900 °C. Subsequently, using the TmIG bulk as the target, an epitaxial film was grown by pulsed laser deposition. Furthermore, the spin transport properties of film with an attached 5 nm-thick platinum layer were studied in terms of longitudinal spin Seebeck effect (LSSE) and spin Hall magnetoresistance (SMR). The LSSE coefficient was as high as 0.38 μV/K and the SMR was 0.0072%. These results indicated that the bulk material and thin film presented excellent qualities, which are extremely important for the fundamental investigation of novel spin transport behaviour in compensated ferrimagnetic insulators. These results also provide more alternatives for spintronic materials.

Alloying-induced spin Seebeck effect and spin figure of merit in Pt-based bimetallic atomic wires of noble metals.

We have investigated using first principles the occurrence and tunability of the spin Seebeck effect in Pt-based bimetallic wires of noble metals (viz. XPt, X = Cu, Ag, and Au) modelled in linear, ladder, and double zigzag (DZZ) topologies. The spin figure of merit ZsT and its charge counterpart ZcT are calculated by considering both electronic and phononic contributions to the thermal conductance. For this endeavour, we have employed the Landauer-Büttiker approach, with the requisite electron τel(E) and phonon τph(E) transmission functions obtained using the non-equilibrium Green's function approach, based on density functional theory and the general utility lattice program, respectively. We find that alloying and/or topological tailoring bring in quantitative as well as qualitative changes in the transport properties. Unlike the pristine wires, τel(E) now depends (except for the CuPt wire in the ladder topology) markedly on spin, thus resulting in an unequal current in the two spin channels and hence a non-zero spin Seebeck coefficient Ss. Remarkably, the AgPt wire in the linear topology and all wires in the DZZ1 and DZZ3 configurations of the DZZ topology exhibit half-metallic conduction, with a sizable gap in the density of ↑-spin states at the Fermi level. Alloying also introduces energy gap(s) in the phonon density of states. Consequently, we find a significant reduction in the electronic and phononic thermal conductance. Interestingly, Ss is of the same order as its charge counterpart Sc, and both can be tuned via the topology and chemical potential μ of the electrodes. This together with the reduced thermal conductance results in a significantly high room-temperature ZcT (∼33) and ZsT (∼25) at μ ∼ 0.24 eV in the AgPt wire in the DZZ3 topology, with about a ten-fold increase in ZcT as compared to the pristine wires. Furthermore, there exists a characteristic μ in some bimetallic wires for which Sc approaches zero, but Ss remains quite appreciable. This result arises due to the emergence of bipolar thermal conduction, which under criticality makes S↑ + S↓ = 0. Importantly, such a situation may be exploited to generate a pure thermal spin voltage. Our results can be explicated on the basis of changes in the electronic band structure and phononic spectra due to alloying and topological effects.

Spin-dependent transport properties and Seebeck effects for a crossed graphene superlattice p-n junction with armchair edge

Using the nonequilibrium Green’s function method combined with the tight-binding Hamiltonian, we theoretically investigate the spin-dependent transmission probability and spin Seebeck coefficient of a crossed armchair-edge graphene nanoribbon (AGNR) superlattice p-n junction under a perpendicular magnetic field with a ferromagnetic insulator, where junction widths W1 of 40 and 41 are considered to exemplify the effect of semiconducting and metallic AGNRs, respectively. A pristine AGNR system is metallic when the transverse layer m = 3j + 2 with a positive integer j and an insulator otherwise. When stubs are present, a semiconducting AGNR junction with width W1 = 40 always shows metallic behavior regardless of the potential drop magnitude, magnetization strength, stub length, and perpendicular magnetic field strength. However, metallic or semiconducting behavior can be obtained from a metallic AGNR junction with W1 = 41 by adjusting these physical parameters. Furthermore, a metal-to-semiconductor transition can be obtained for both superlattice p-n junctions by adjusting the number of periods of the superlattice. In addition, the spin-dependent Seebeck coefficient and spin Seebeck coefficient of the two systems are of the same order of magnitude owing to the appearance of a transmission gap, and the maximum absolute value of the spin Seebeck coefficient reaches 370 µV/K when the optimized parameters are used. The calculated results offer new possibilities for designing electronic or heat-spintronic nanodevices based on the graphene superlattice p-n junction.

Spin Current Noise of the Spin Seebeck Effect and Spin Pumping.

We theoretically investigate the fluctuation of a pure spin current induced by the spin Seebeck effect and spin pumping in a normal-metal-(NM-)ferromagnet(FM) bilayer system. Starting with a simple ferromagnet-insulator-(FI-)NM interface model with both spin-conserving and non-spin-conserving processes, we derive general expressions of the spin current and the spin-current noise at the interface within second-order perturbation of the FI-NM coupling strength, and estimate them for a yttrium-iron-garnet-platinum interface. We show that the spin-current noise can be used to determine the effective spin carried by a magnon modified by the non-spin-conserving process at the interface. In addition, we show that it provides information on the effective spin of a magnon, heating at the interface under spin pumping, and spin Hall angle of the NM.

Spin and Charge Caloritronics in Bilayer Graphene Flakes with Magnetic Contacts

We investigate the coupling of spin and thermal currents as a means to rise the thermoelectric efficiency of nanoscale graphene devices. We consider nanostructures composed of overlapping graphene nanoribbons with ferromagnetic contacts in different magnetic configurations. Our results show that the charge Seebeck effect is greatly enhanced when the magnetic leads are in an antiparallel configuration, due to the enlargement of the transport gap. However, for the optimization of the charge figure of merit ZT it is better to choose a parallel alignment of the magnetization in the leads, because the electron-hole symmetry is broken in this magnetic configuration. We also obtain the spin-dependent Seebeck coefficient and spin figure of merit. In fact, the spin ZT can double its value with respect to the charge ZT for a wide temperature range, above 300 K. These findings suggest the potential value of graphene nanosystems as energy harvesting devices employing spin currents.

Edge-defect induced spin-dependent Seebeck effect and spin figure of merit in graphene nanoribbons.

By using the first-principle calculations combined with the non-equilibrium Green's function approach, we have studied spin caloritronic properties of graphene nanoribbons (GNRs) with different edge defects. The theoretical results show that the edge-defected GNRs with sawtooth shapes can exhibit spin-dependent currents with opposite flowing directions by applying temperature gradients, indicating the occurrence of the spin-dependent Seebeck effect (SDSE). The edge defects bring about two opposite effects on the thermal spin currents: the enhancement of the symmetry of thermal spin-dependent currents, which contributes to the realization of pure thermal spin currents, and the decreasing of the spin thermoelectric conversion efficiency of the devices. It is fortunate that applying a gate voltage is an efficient route to optimize these two opposite spin thermoelectric properties towards realistic device applications. Moreover, due to the existence of spin-splitting band gaps, the edge-defected GNRs can be designed as spin-dependent Seebeck diodes and rectifiers, indicating that the edge-defected GNRs are potential candidates for room-temperature spin caloritronic devices.

Tm3Fe5O12/Pt Heterostructures with Perpendicular Magnetic Anisotropy for Spintronic Applications

With recent developments in the field of spintronics, ferromagnetic insulator (FMI) thin films have emerged as an important component of spintronic devices. Ferrimagnetic yttrium iron garnet in particular is an excellent insulator with low Gilbert damping and a Curie temperature well above room temperature, and has been incorporated into heterostructures that exhibit a plethora of spintronic phenomena including spin pumping, spin Seebeck, and proximity effects. However, it has been a challenge to develop high quality sub‐10 nm thickness FMI garnet films with perpendicular magnetic anisotropy (PMA) and PMA garnet/heavy metal heterostructures to facilitate advances in spin‐current and anomalous Hall phenomena. Here, robust PMA in ultrathin thulium iron garnet (TmIG) films of high structural quality down to a thickness of 5.6 nm are demonstrated, which retain a saturation magnetization close to bulk. It is shown that TmIG/Pt bilayers exhibit a large spin Hall magnetoresistance (SMR) and SMR‐driven anomalous Hall effect, which indicates efficient spin transmission across the TmIG/Pt interface. These measurements are used to quantify the interfacial spin mixing conductance in TmIG/Pt and the temperature‐dependent PMA of the TmIG thin film.

Spin Seebeck effect through antiferromagnetic NiO

We report temperature-dependent spin-Seebeck measurements on Pt/YIG bilayers and Pt/NiO/YIG trilayers, where YIG (Yttrium iron garnet, Y$_3$Fe$_5$O$_{12}$) is an insulating ferrimagnet and NiO is an antiferromagnet at low temperatures. The thickness of the NiO layer is varied from 0 to 10 nm. In the Pt/YIG bilayers, the temperature gradient applied to the YIG stimulates dynamic spin injection into the Pt, which generates an inverse spin Hall voltage in the Pt. The presence of a NiO layer dampens the spin injection exponentially with a decay length of $2 \pm 0.6$ nm at 180 K. The decay length increases with temperature and shows a maximum of $5.5 \pm 0.8$ nm at 360 K. The temperature dependence of the amplitude of the spin-Seebeck signal without NiO shows a broad maximum of $6.5 \pm 0.5$ $\mu$V/K at 20 K. In the presence of NiO, the maximum shifts sharply to higher temperatures, likely correlated to the increase in decay length. This implies that NiO is most transparent to magnon propagation near the paramagnet-antiferromagnet transition. We do not see the enhancement in spin current driven into Pt reported in other papers when 1-2 nm NiO layers are sandwiched between Pt and YIG.

Phenomenological Spin Transport Theory Driven by Anomalous Nernst Effect

Several experimental efforts such as material investigation and structure improvement have been made recently to find a large anomalous Nernst effect in ferromagnetic metals. Here, we develop a theory of spin transport driven by the anomalous Nernst effect in a diffusive ferromagnetic/nonmagnetic multilayer. Starting from a phenomenological formula of a spin-dependent electric current, the theoretical formulas of electric voltage and spin torque generated by the anomalous Nernst effect are derived. The magnitude of the electric voltage generated from the spin current via the inverse spin Hall effect is on the order of $0.1$ $\mu$V for currently available experimental parameter values. The temperature gradient necessary to switch the magnetization is quite larger than the typical experimental value. The separation of the contributions of the Seebeck and transverse spin Seebeck effects is also discussed.

Spin-Swapping Transport and Torques in Ultrathin Magnetic Bilayers.

Planar spin transport in disordered ultrathin magnetic bilayers comprising a ferromagnet and a normal metal (typically used for spin pumping, spin Seebeck and spin-orbit torque experiments) is investigated theoretically. Using a tight-binding model that puts the extrinsic spin Hall effect and spin swapping on equal footing, we show that the nature of spin-orbit coupled transport dramatically depends on the ratio between the layer thickness d and the mean free path λ. While the spin Hall effect dominates in the diffusive limit (d≫λ), spin swapping dominates in the Knudsen regime (d≲λ). A remarkable consequence is that spin swapping induces a substantial fieldlike torque in the Knudsen regime.

Strong modification of intrinsic spin Hall effect in FeMn with antiferromagnetic order formation

FeMn films with and without a Cu seed layer were deposited on Y3Fe5O12 (YIG) substrates, and their inverse spin Hall effect (ISHE) was examined through both spin Seebeck effect and spin pumping.

Spin Seebeck Power Conversion

Spin caloritronics is the science and technology to control spin, charge, and heat currents in magnetic nanostructures. The spin degree of freedom provides new strategies for thermolelectric power generation that have not yet been fully explored. After an elementary introduction into conventional thermoelectrics and spintronics, we give a brief review of the physics of spin caloritronics. We discuss spin-dependent thermoelectrics based on the the two-current model in metallic magnets as well as the spin Seebeck and Peltier effects that are based on spin wave excitations in ferromagnets. We derive expressions for the efficiency and figure of merit ZT of several spin caloritronic devices.

Spin-dependent Seebeck effect and spin caloritronics in magnetic graphene

We investigate the spin-dependent thermoelectric effects in magnetic graphene in both diffusive and ballistic regimes. Employing the Boltzmann and Landauer formalisms we calculate the spin and charge Seebeck coefficients (thermopower) in magnetic graphene varying the spin splitting, temperature, and doping of the junction. It is found that while in normal graphene the temperature gradient drive a charge current, in the case of magnetic graphene a significant spin current is also established. In particular we show that in the undoped magnetic graphene in which different spin carriers belong to conduction and valence bands, a pure spin current is driven by the temperature gradient. In addition it is revealed that profound thermoelectric effects can be achieved at intermediate easily accessible temperatures when the thermal energy is comparable with Fermi energy $k_BT\lesssim \mu$. By further investigation of the spin-dependent Seebeck effect and a significantly large figure of merit for spin thermopower $\mathcal{Z}_{\rm sp}T$, we suggest magnetic graphene as a promising material for spin-caloritronics studies and applications.

Spin Seebeck effect and spin Hall magnetoresistance at high temperatures for a Pt/yttrium iron garnet hybrid structure.

Based on unique experimental setups, the temperature dependences of the longitudinal spin Seebeck effect (LSSE) and spin Hall magnetoresistance (SMR) of the Pt/yttrium iron garnet (Pt/YIG) hybrid structure are determined in a wide temperature range up to the Curie temperature of YIG. From a theoretical analysis of the experimental relationship between the SMR and temperature, the spin mixing conductance of the Pt/YIG interface is deduced as a function of temperature. Adopting the deduced spin mixing conductance, the temperature dependence of the LSSE is well reproduced based on the magnon spin current theory. Our research sheds new light on the controversy about the theoretical models for the LSSE.

Joule heating-induced coexisted spin Seebeck effect and spin Hall magnetoresistance in the platinum/Y3Fe5O12 structure

Spin Seebeck effect (SSE) and spin Hall magnetoresistance (SMR) are observed simultaneously in the Pt/Y3Fe5O12 hybrid structure when thermal gradient is produced by Joule heating. According to their dependences on applied current, these two effects can be separated. Their dependence on heating power and magnetic field is systematically studied. With the increase of heating power, the SSE enhances linearly, whereas the SMR decreases slowly. The origin of the spin currents is further analyzed. The heating power dependences of the spin currents associated with the SSE and the SMR are found to be different.

Nanoscale Spin Seebeck Rectifier: Controlling Thermal Spin Transport across Insulating Magnetic Junctions with Localized Spin

The spin Seebeck effect is studied across a charge insulating magnetic junction, in which thermal-spin conjugate transport is assisted by the exchange interactions between the localized spin in the center and electrons in metallic leads. We show that, in contrast with bulk spin Seebeck effect, the figure of merit of such nanoscale thermal-spin conversion can be infinite, leading to the ideal Carnot efficiency in the linear response regime. We also find that in the nonlinear spin Seebeck transport regime, the device possesses the asymmetric and negative differential spin Seebeck effects. In the last, the situations with leaking electron tunneling are also discussed. This nanoscale thermal spin rectifier, by tuning the junction parameters, can act as a spin Seebeck diode, spin Seebeck transistor and spin Seebeck switch, which could have substantial implications for flexible thermal and information control in molecular spin caloritronics.

Advanced Thermoelectrics: From Materials to Devices

The development of advanced thermoelectric materials for efficient thermoelectric devices is a major challenge in energy conversion technologies. To overcome limitations of toxic and expensive state-of-the-art bulk semiconductors, an improved fundamental understanding of the materials properties and of the thermoelectric conversion processes is needed. At the Symposium "Advanced Thermoelectrics: From Materials to Devices" held at the E-MRS Spring 2013 conference, May 27–31, 2013, Strasbourg, France the topic of thermoelectricity was discussed from a very broad perspective. Not only was the subtitle – from materials to devices – taken very literally, but also were other axes explored, from simple model materials to materials of extreme complexity, from plastics to borides, from chemical to solid state synthesis, from electrochemical thin film deposition to molecular beam epitaxy, from nanoparticles to nanocomposites, from lab-scale to large-scale materials fabrication, from steady state to time resolved measurements, from conventional thermoelectric concepts to entirely new approaches, from phonon to electron engineering, from molecular dynamics simulations to strongly correlated band theory, from degradation to encapsulation, from micro- to macro-devices. This breadth of topics is also reflected in this special issue. Many different materials classes are covered. Graphene, bismuth, silicon, bismuth tellurides and antimonides, lead tellurides, half-Heusler compounds, oxides, chalcogenides, oxy-chalcogenides, borides, skutterudites, clathrates, complex Zintl compounds, Kondo insulators, topological insulators, organic conductors, glasses, phase change materials, CrN. Most of these materials are investigated as bulk single or polycrystals or as single or polycrystalline thick or thin films. Some of the materials are also investigated as nano- or microwires, nanosheets, or membranes. While some articles focus on the bare intrinsic materials properties, most of them present optimization studies. Many different concepts (electron and phonon engineering) and techniques are explored to improve the thermoelectric efficiency of a given material, frequently leading to interesting ZT values of the order of 1 to 1.5 in varying temperature ranges: doping/substitutions (up to pentenary compounds!), nanograin formation, phase separation, strain/shear, introduction of precipitates (including for instance C60), fabrication of composites, fabrication of ordered and even aperiodic heterostructures, superlattices and quantum dots, sometimes based on different isotopes, etc. It becomes more and more common to study also the stability of the materials and in particular of their artificial nano/microstructuring upon thermal cycling. However, real long term studies have not been presented. Instead, many different strategies are explored to stabilize the structures. On the characterization side, the spectrum has broadened considerably. While the standard steady state techniques to measure the thermoelectric quantities of bulk samples are still broadly used, alternative techniques are getting more widespread, e.g., scanning thermal probe micro-imaging, the 3-omega technique, laser flash diffusivity measurements, time domain thermal reflectance, pump-probe techniques, Raman thermometry, and others. Some articles also deal with the fabrication of devices. The progress on microgenerators, frequently based on nanostructures, is impressive. Also a number of traditional thermoelectric generators, fabricated typically from compacted and sintered powders, are discussed. Some presentations also address upscaling. The integration of thermoelectric modules into automobiles and roadmaps to the targeted efficiencies and cost levels are another important issue. Furthermore also entirely new approaches to explore thermoelectric effects for energy generation are discussed, e.g., pn junction thermoelectric generators, thermionic converters, spin Seebeck plus spin Hall effect generators, and liquid chemical thermocouples. And finally, just a few highlights: A new world record in thermoelectric efficiency of clathrates over the relevant temperature range was shown. An entirely new thermoelectric device concept based on spin current plus spin Hall effect was presented and realized in a microgenerator. The simultaneous drastic enhancement of the electrical conductivity and the thermopower in half-Heusler compounds by certain additives was demonstrated. The symposium as well as this special issue is a testimony of great worldwide activity in the field of advanced thermoelectrics. A waste amount of different subtopics are addressed by a broad community. The results are getting more reliable and reproducible, application relevant issues are considered by an increasing number of scientists. Overall, there is hope in the community that thermoelectric applications in waste heat generation will not remain a dream. The symposium was financially supported by INTELBIOMAT (European Science Foundation) and the Swiss Federal Office of Energy (SFOE). The symposium organizers Silke Buehler-Paschen, Antonio Pereira Gonçalves, Sascha Populoh, and Jan D. König

Voltage tuning of thermal spin current in ferromagnetic tunnel contacts to semiconductors

Spin currents are paramount to manipulate the magnetization of ferromagnetic elements in spin-based memory, logic and microwave devices, and to induce spin polarization in non-magnetic materials. A unique approach to create spin currents employs thermal gradients and heat flow. Here we demonstrate that a thermal spin current can be tuned conveniently by a voltage. In magnetic tunnel contacts to semiconductors (silicon and germanium), it is shown that a modest voltage (~200 mV) changes the thermal spin current induced by Seebeck spin tunnelling by a factor of five, because it modifies the relevant tunnelling states and thereby the spin-dependent thermoelectric parameters. The magnitude and direction of the spin current is also modulated by combining electrical and thermal spin currents with equal or opposite sign. The results demonstrate that spin-dependent thermoelectric properties away from the Fermi energy are accessible, and open the way towards tailoring thermal spin currents and torques by voltage, rather than material design.

Thermal creation of electron spin polarization in n-type silicon

Conversion of heat into a spin-current in electron doped silicon can offer a promising path for spin-caloritronics. Here, we create an electron spin polarization in the conduction band of n-type silicon by producing a temperature gradient across a ferromagnetic tunnel contact. The substrate heating experiments induce a large spin signal of 95 μV, corresponding to 0.54 meV spin-splitting in the conduction band of n-type silicon by Seebeck spin tunneling mechanism. The thermal origin of the spin injection has been confirmed by the quadratic scaling of the spin signal with the Joule heating current and linear dependence with the heating power.